1. Field of the Invention
The present invention relates to semiconductor materials and, more particularly, to determining a diffusion length of a minority carrier in a semiconductor material.
2. Description of Related Art
When a semiconductor material is processed, it may become contaminated, during one or more processing steps, by a heavy metal, such as iron, for example. Such contamination degrades the semiconductor material, as the contaminants act as recombination centers which eliminate charge carriers in the semiconductor material.
Commonly, contaminants are detected by determining a minority carrier diffusion length of a semiconductor material, which is the distance a minority carrier moves during its lifetime.
To determine a minority carrier diffusion length in a material, minority carriers can be generated in the material by applying an excitation light, such as a laser, to a surface of the material. The number of minority carriers N (also referred to as carrier concentration) that reach the surface of the material as a result of the excitation light is proportional to a photon flux I of the excitation light, and depends on a penetration depth d of the excitation light and the minority carrier diffusion length L of the material. The relationship between L, I, N and d can be described by the following equation:
                              I                                    (                              d                +                L                            )                        ⁢            N                          =        const                            (        1        )            
The penetration depth d of a material is related to a wavelength λ of the excitation light. For example, the relationship between the penetration depth d of silicon and an excitation wavelength λ can be described by the equation:
                    d        =                  1                                    (                                                83.15                  /                  λ                                -                74.87                            )                        2                                              (        2        )            
The minority carrier diffusion length L of a given material can be determined if the carrier concentration N for two different penetration depths can be measured. That is, since:
                                                        I              1                                                      (                                                      d                    1                                    +                  L                                )                            ⁢                              N                1                                              =                                    I              2                                                      (                                                      d                    2                                    +                  L                                )                            ⁢                              N                2                                                    ,                            (        3        )            then L can be determined from the equation:
                    L        =                                                            d                2                            ⁢                                                I                  1                                /                                  N                  1                                                      -                                          d                1                            ⁢                                                I                  2                                /                                  N                  2                                                                                                        I                2                            /                              N                2                                      -                                          I                1                            /                              N                1                                                                        (        4        )            
However, the carrier concentration N cannot be measured directly. Rather, N must be determined by measuring a surface photo voltage V of the material, which results from electron-hole pairs reaching the proximity of the surface. The relationship between the carrier concentration N and the surface photo voltage V of a material is complicated, but can be approximated by the parametric formula:N=const(eAV−1+SV),  (5)in which A and S are parameters which correspond to properties of the material. A is related to band bending and bandwidth, and S expresses surface recombination. However, the parameters A and S are not stable values. A and S vary with time and have different values at different locations of the material, especially when the material is exposed to light. Unfortunately, illuminating the material with a measurement light can change these parameters.
A known conventional method of determining a minority carrier diffusion length L of a material, described in U.S. Pat. No. 4,333,051, and referred to here as a “Constant Voltage Approach”, is described as follows. The theories behind the Constant Voltage Approach are that, if N1=N2, equation (4) can be simplified to:
                    L        =                                                            d                2                            ⁢                              I                1                                      -                                          d                1                            ⁢                              I                2                                                                        I              2                        -                          I              1                                                          (        6        )            and if N1=N2, then V1=V2. The dependency between V and N is assumed to be constant in time and not impacted by the illumination of a material with a measurement excitation light.
Thus, in the Constant Voltage Approach, a first excitation light having a photon flux I1, is applied to a subject material at a penetration depth d1. A surface photo voltage V1 is then measured. Next, a second excitation light is applied to the material at a penetration depth d2. The photon flux I2 of the second excitation light is then adjusted until a resulting surface photo voltage V2 is equal to V1. The photon flux I2 which generates the surface photo voltage V2 is then measured. Once the values I1, d1, I2 and d2 are known, the minority carrier diffusion length L of the material can be determined, using equation (6).
However, a flaw of the Constant Voltage Approach is that the adjustment of the photon flux of the second excitation light required by the approach results in a relatively long measurement time. Since the parameters A and S are time dependent, they may change between the measurements of I1 and I2, which results in significant measurement errors. That is, the theory that N1 will equal N2 if V1 equals V2 will not be true, if A or S change between measurements.
A second conventional method of determining a minority carrier diffusion length L of a material, described in U.S. Pat. No. 5,177,351, and referred to here as a “Linear Constant Flux Approach”, is described as follows. The Linear Constant Flux Approach does not require time-consuming photon flux adjustment, and thus is faster than the Constant Voltage Approach. Under the Linear Constant Flux Approach, the photon flux of the excitation light is kept constant during the measurement process; that is, I1=I2. Thus, equation (4) reduces to:
                    L        =                                                            d                2                            ⁢                              N                2                                      -                                          d                1                            ⁢                              N                1                                                                        N              1                        -                          N              2                                                          (        7        )            
Assuming that the surface photo voltage V is linearly related to photon flux I and carrier concentration N, equation (7) leads to:
                    L        =                                                            d                2                            ⁢                              V                2                                      -                                          d                1                            ⁢                              V                1                                                                        V              1                        -                          V              2                                                          (        8        )            For this to be true, the measurement must be carried out at a low enough excitation, so that equation (5) can be replaced by a linear approximation. Unfortunately, voltages are practically immeasurable at such a low excitation.
Thus, the Linear Constant Flux Approach must be performed at elevated voltages V1 and V2 which then fall within the non-linear range of the V-N relationship, in which equation (8) is inaccurate.
In praxis, the excitation level is adjusted to set a certain level of non-linearity of the V-N-relationship. This is done by using a set of two filters of known intensity ratio 2.0 at the same wavelength and adjusting the overall excitation light intensity until a voltage ratio of typically 1.8 is measured. This is done once at a sample center and the light intensity is then fixed for the remaining measurement. It is assumed that at this fixed light intensity the non-linearity is the same at all measurement sites and does not change in time or under exposure to measurement light. Under these assumptions, it is believed that the resulting inaccuracy in equation (8) can be compensated by calibrating the system under the same level of non-linearity.
However, under practical conditions the non-linearity does change under the influence of the measurement light and is different at different measurement sites, causing significant measurement errors. Thus, the Linear Constant Flux Approach suffers from non-linearity errors in addition to errors resulting from the V-N-relation changes between switching light sources.
Another invention, described in U.S. Pat. No. 6,512,384, addresses the problem of the changing V-N-relation between switching light sources by simultaneously measuring the various voltages of different wavelengths. This is done by modulating each light source at a different frequency and illuminating the sample simultaneously with each wavelength. The individual voltages are then extracted from the resulting voltage signal by using harmonic analysis.
This method solves the problem of the changing V-N-relation in time, however, it complicates the non-linearity problem by superimposing several differently modulated photon fluxes. For instance, by using two wavelengths individually producing similar amounts of N at the surface, the peak values of the resulting combined N will reach twice the level. Unfortunately, this will worsen the non-linearity measurement error. In addition, it will enhance measurement artifacts caused by the time dependency of the V-N-relation under light exposure. In addition, by using different modulation frequencies, this method is very likely susceptible to phase shift-frequency dependencies, leading to previously non-existing problems.
Another invention, described in U.S. Pat. No. 6,526,372, also addresses the problem of the V-N-relation time and dependency by simultaneously applying and measuring the various voltages of different wavelengths. However, unlike in U.S. Pat. No. 6,512,384, it does so by a special modulation method that is alternating the various light sources and dark phase in a cyclic fashion, without ever exposing the sample to more than one light source at a time. Thereby, this method avoids enhanced non-linearity error as well as the phase-shift error of the method described in U.S. Pat. No. 6,512,384, but still suffers from the same level of non-linearity error as the Linear Constant Flux Approach.
Another invention, described in U.S. Pat. No. 7,026,831, addresses both original problems, the non-linearity and time dependency under light exposure of the V-N-relation. It does this by alternating the excitation between the different wavelengths and adjusting the individual intensities until the resulting surface potential modulation disappears. The resulting intensities are then used to calculate the diffusion length based on equation (6). Unlike the Constant Voltage Approach, this method is completely insensitive to V-N-relation details, since it does not even measure individual voltages. It works somewhat similar to a compensation bridge measurement, only making sure each light source generates exactly the same N. This fact further allows the use of higher excitation levels, if necessary.
Like the Constant Voltage Approach, this method also involves a time-consuming adjustment of intensities at each measurement site and is therefore potentially slower than methods that work with fixed intensities and only rely on voltage measurements.